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Positive-Definite and Monotonic Limiters for Unrestricted-Time-Step Transport Schemes

William C. Skamarock
2006 Monthly Weather Review  
General positive-definite and monotonic limiters are described for use with unrestricted-Courant-number flux-form transport schemes.  ...  These limiters are tested using a time-split multidimensional transport scheme.  ...  FIG. 4 . 4 Results for the positive-definite limiter for Courant numbers (a) Cr max ϭ 1 and (b) Cr max ϭ 4.  ... 
doi:10.1175/mwr3170.1 fatcat:kvocgv5difa7zbqauizrh4vv24

A numerical method for solving a scalar advection-dominated transport equation with concentration-dependent sources

Minghui Jin, Roseanne M. Ford, Peter T. Cummings
2003 Computers and Chemical Engineering  
A numerical scheme, upstream biased Eulerian algorithm for transport equations with sources (UpBEATES), is developed for solving a scalar advective-dominated transport equation with concentration-independent  ...  The proposed scheme is mass-conservative, produces non-negative concentration values, exhibits low numerical dispersion, and is efficient for advection-dominated problems with concentration-dependent source  ...  We thank Kevin Chen for recommending the Bott's scheme, and for introducing the FCT literature to us.  ... 
doi:10.1016/s0098-1354(03)00008-5 fatcat:arnsnkkauna4latar6wyn5s4ty

Design and experiments of a new positive-definite renormalization scheme for advection-diffusion differential equation

Hao Shi-Feng, Cui Xiao-Peng
2012 Wuli xuebao  
Experiments of point-source advectiondiffusion show that the new renormalization scheme not only solves the positive-definite problem of advection-diffusion differential equation, but also keeps the property  ...  Total mass conservation is a basic property of advection-diffusion differential equation.  ...  Design and experiments of a new positive-definite renormalization scheme for advection-diffusion differential equation * , . k∇ 2 µφ, k .  ... 
doi:10.7498/aps.61.039204 fatcat:5jzim6g34jcyno6f73aq2fjysa

Stabilized element residual method (SERM): A posteriori error estimation for the advection-diffusion equation

Amit N. Agarwal, Peter M. Pinsky
1996 Journal of Computational and Applied Mathematics  
Residual-based a posteriori error estimation techniques have been developed for linear elliptic symmetric positive-definite problems.  ...  This technique is extended to the unsymmetric and positive semi-definite advection-diffusion (AD) operator. Here, a novel approach, the Stabilized Element Residual Method (SERM) is presented.  ...  While numerous authors have considered a posteriori error estimates for linear, elliptic, self-adjoint and positive-definite problems, the AD equation has received limited treatment.  ... 
doi:10.1016/0377-0427(96)00014-3 fatcat:oxbndpjeyng7lhb7oyussbrsry

Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM)

P. E. Haines, J. G. Esler, G. D. Carver
2014 Atmospheric Chemistry and Physics  
These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux limiters in the advection scheme are not required.  ...  </strong> A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model, RETRO-TOM.  ...  Given our definition (see comment 2) our statement that "accurate adjoint calculations are rendered near-impossible by advective nonlinearities such as flux limiters" is correct.  ... 
doi:10.5194/acp-14-5477-2014 fatcat:ekhrsqqxkjgu5ezynqylda5br4

A second-order realizable scheme for moment advection on unstructured grids

Alberto Passalacqua, Frédérique Laurent, Rodney O. Fox
2019 Computer Physics Communications  
"A second-order realizable scheme for moment advection on unstructured grids Abstract The second-order realizable moment advection scheme developed in Laurent and Nguyen (2017) is extended to the case  ...  Chemical Engineering | Physics Comments Comments This is a manuscript of an article published as Passalacqua, Alberto, Frédérique Laurent, and Rodney O. Fox.  ...  The definition of the limiter function for a minmod limiter is [66, 71] : ℒ( f ) = max(0, min(1, f )). (4.3) The evaluation of the gradient of over the cell C in Eq. (4.2) is detailed in Darwish and Moukalled  ... 
doi:10.1016/j.cpc.2019.106993 fatcat:sgw2pp2gljhlhj2dcl5y223uiq

Monotonicity, positivity and strong stability of the TR-BDF2 method and of its SSP extensions [article]

Luca Bonaventura, Alessandro Della Rocca
2015 arXiv   pre-print
The results show that both strategies provide a good compromise between accuracy and robustness at high CFL numbers, without suffering from the limitations of alternative approaches already available in  ...  We analyze the one-step method TR-BDF2 from the point of view of monotonicity, strong stability and positivity.  ...  The range of the test cases covers a reactive zero dimensional test problem, here adapted to the MPRK method, a one dimensional advection problem, an advection diffusion reaction problem for a mixture  ... 
arXiv:1510.04303v1 fatcat:24khb3zkfvd6nezg47m3ma2odu

The non-monotonicity of the KPP speed with respect to diffusion in the presence of a shear flow

Mohammad El Smaily
2013 Proceedings of the American Mathematical Society  
For the sake of completeness, we announce our results in a setting which allows domains with periodic perforations that may or may not be equal to the whole space R N .  ...  In this paper, we prove via counterexamples that adding an advection term of the form Shear flow (whose streamlines are parallel to the direction of propagation) to a reaction-diffusion equation will be  ...  The author would also like to thank him for his valuable, fruitful and precise suggestions while reading a preprint of this work.  ... 
doi:10.1090/s0002-9939-2013-11728-4 fatcat:zms6uvuaifcb7hetlhprzjyaca

A Lagrangian Advection Scheme Using Tracer Points

Eigil Kaas, Annette Guldberg, Philippe Lopez
1997 ATMOSPHERE-OCEAN  
As it is intended to use the FPIC scheme for advection of water vapour and liquid water in a GCM, a test of advection of a positive definite, sharply varying, passive tracer in the shallow water mode1  ...  Furthermore, the scheme is positive dejïnite. The most serious limitation of the scheme is that if demands more memory than traditional schemes.  ...  Acknowledgements The work presented in this paper was carried out within a joint Nordic CLimate Modelling Project, NOCLIMP, funded by the Nordic Council of Ministers (project number FS/ULF/93002).  ... 
doi:10.1080/07055900.1997.9687347 fatcat:l64ghd2f4zbbve5beer2ed2jtq

Material barriers to diffusive and stochastic transport

George Haller, Daniel Karrasch, Florian Kogelbauer
2018 Proceedings of the National Academy of Sciences of the United States of America  
Even in the limit of vanishing diffusivity, these surfaces differ from all previously identified coherent structures for purely advective fluid transport.  ...  We seek transport barriers and transport enhancers as material surfaces across which the transport of diffusive tracers is minimal or maximal in a general, unsteady flow.  ...  x0) of the positive definite tensorCD(x0).  ... 
doi:10.1073/pnas.1720177115 pmid:30150387 fatcat:wfjyt4tplvgkzjbezt56ok5fsq

Finite difference TVD scheme for modeling two-dimensional advection-dispersion [chapter]

Y Guan, D Zhang
2004 Environmental Hydraulics and Sustainable Water Management, Two Volume Set  
Both the numerical tests and model application show that the TVD schemes are very competent for solving the advection-dominated transport problems.  ...  Due to various limiters owning different features, the numerical tests for 1D pure advection and 2D dispersion are conducted to evaluate the performance of different TVD schemes firstly, then the TVD schemes  ...  defined as i max[0, min(2, 2r), 0.5(1 r)] φ = + (10) These limiters are considerably simple; as a result, they are often used for solving the advection problems.  ... 
doi:10.1201/b16814-83 fatcat:n6tk4phigbfcrp2y5epb4mlmtm

On finite element method–flux corrected transport stabilization for advection–diffusion problems in a partial differential–algebraic framework

Julia Vuong, Bernd Simeon
2014 Journal of Computational and Applied Mathematics  
Numerical results are presented for nonconstant and time-dependent boundary conditions in one space dimension and for a two-dimensional advection problem where the advection proceeds skew to the mesh.  ...  Given a local extremum diminishing property of the spatial discretization, the positivity preservation of the one-step θ−scheme when applied to the time integration of the resulting differentialalgebraic  ...  Moreover, we are grateful to Matthias Möller for helpful discussions and hints on the FEM-FCT scheme.  ... 
doi:10.1016/j.cam.2013.09.070 fatcat:u2blj7m6jzch7ixohqi6qgiyte

Polynomial Level-Set Method for Polynomial System Reachable Set Estimation

Ta-Chung Wang, Sanjay Lall, Matthew West
2013 IEEE Transactions on Automatic Control  
The problem of flowing these sets under the advection map of a dynamical system is converted to a semi-definite program, which is then used to compute the coefficients of the polynomials.  ...  In this paper, we present a polynomial level-set method for advecting a semi-algebraic set for polynomial systems. This method uses the sub-level representation of sets.  ...  Suppose there exists a positively definite matrix , and that solve the following optimization problem Then gives the best quadratic fitting of in the sense of relative radial error. Proof: Clearly .  ... 
doi:10.1109/tac.2013.2263916 fatcat:zmlevb7plvgxxnpxglhwpiglhi

The multidimensional positive definite advection transport algorithm: nonoscillatory option

Piotr K Smolarkiewicz, Wojciech W Grabowski
1990 Journal of Computational Physics  
In responding to such practical needs, we present an option of the multidimensional positive definite advection transport algorithm (hereinafter, MPDATA) which strictly preserves the local monotone character  ...  In a number of applications, monotonicity preservation becomes a necessary property of the advection scheme.  ...  The nonoscillatory option of the multidimensional positive definite advection transport algorithm (MPDATA) was presented.  ... 
doi:10.1016/0021-9991(90)90105-a fatcat:mryrbj524rg4fbcbfxk5xsv5k4

The non-monotonicity of the KPP speed with respect to diffusion in the presence of a shear flow [article]

Mohammad El Smaily
2011 arXiv   pre-print
For the sake of completeness, we announce our results in a setting which allows domains with periodic perforations that may or may not be equal to the whole space R^N.  ...  In this paper, we prove via counterexamples that adding an advection term of the form Shear flow (whose streamlines are parallel to the direction of propagation) to a reaction-diffusion equation will be  ...  Also, I would like to thank him for his valuable, fruitful and precise suggestions while reading a preprint of this work.  ... 
arXiv:1103.0052v2 fatcat:ulgtdavuqvbn7kbb4sf6mx4pru
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